Problem: On the way to school, Karen became fixated on the puzzle game on her phone!

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The game is played as follows. In each level, you have a grid with n rows and m columns. Each cell originally contains the number 0.

One move consists of choosing one row or column, and adding 1 to all of the cells in that row or column.

To win the level, after all the moves, the number in the cell at the i-th row and j-th column should be equal to gi, j.

Karen is stuck on one level, and wants to know a way to beat this level using the minimum number of moves. Please, help her with this task!

Input

The first line of input contains two integers, n and m (1 ≤ n, m ≤ 100), the number of rows and the number of columns in the grid, respectively.

The next n lines each contain m integers. In particular, the j-th integer in the i-th of these rows contains gi, j (0 ≤ gi, j ≤ 500).

Output

If there is an error and it is actually not possible to beat the level, output a single integer -1.

Otherwise, on the first line, output a single integer k, the minimum number of moves necessary to beat the level.

The next k lines should each contain one of the following, describing the moves in the order they must be done:

  * row x, (1 ≤ x ≤ n) describing a move of the form "choose the x-th row". 
  * col x, (1 ≤ x ≤ m) describing a move of the form "choose the x-th column". 



If there are multiple optimal solutions, output any one of them.

Examples

Input

3 5
2 2 2 3 2
0 0 0 1 0
1 1 1 2 1


Output

4
row 1
row 1
col 4
row 3


Input

3 3
0 0 0
0 1 0
0 0 0


Output

-1


Input

3 3
1 1 1
1 1 1
1 1 1


Output

3
row 1
row 2
row 3

Note

In the first test case, Karen has a grid with 3 rows and 5 columns. She can perform the following 4 moves to beat the level:

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In the second test case, Karen has a grid with 3 rows and 3 columns. It is clear that it is impossible to beat the level; performing any move will create three 1s on the grid, but it is required to only have one 1 in the center.

In the third test case, Karen has a grid with 3 rows and 3 columns. She can perform the following 3 moves to beat the level:

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Note that this is not the only solution; another solution, among others, is col 1, col 2, col 3.

Solution (in PYTHON3):

Solution:
n, m = map(int, input().split())

array = []
row_sums = [0 for x in range(n)]

for i in range(n):
	array.append(list(map(int, input().split())))
	row_sums[i] = sum(array[i])

col_sums = [sum(x) for x in zip(*array)]

min_row_index = row_sums.index(min(row_sums))
min_col_index = col_sums.index(min(col_sums))


row_boost = [0 for x in range(n)]
col_boost = [0 for x in range(m)]
#rows contribute more
if n <= m:
	#get largest row add possible
	col_boost[min_col_index] = 0
	for i in range(m):
		if i != min_col_index:
			col_boost[i] = (col_sums[i] - col_sums[min_col_index]) // n

		sum_col_boosts = sum(col_boost)

		for i in range(n):
			row_boost[i] = (row_sums[i] - sum_col_boosts) // m

if n >= m:
	row_boost[min_row_index] = 0

	for i in range(n):
		if i != min_row_index:
			row_boost[i] = (row_sums[i] - row_sums[min_row_index]) // m

	sum_row_boosts = sum(row_boost)

	for i in range(m):
		col_boost[i] = (col_sums[i] - sum_row_boosts) // n

for row in range(n):
	if [row_boost[row] + c for c in col_boost] != array[row]:
		print(-1)
		exit()

print(sum(row_boost + col_boost))
for i in range(n):
	for count in range(row_boost[i]):
		print('row ' + str(i+1))

for j in range(m):
	for count in range(col_boost[j]):
		print('col ' + str(j+1))